Force-free magnetic fields - Generating functions and footpoint displacements

This paper presents analytic and numerical calculations that explore equilibrium sequences of bipolar force-free magnetic fields in relation to displacments of their magnetic footpoints. It is shown that the appearance of magnetic islands - sometimes interpreted as marking the loss of equilibrium in models of the solar atmosphere - is likely associated only with physically unrealistic footpoint displacements such as infinite separation or 'tearing' of the model photosphere. The work suggests that the loss of equilibrium in bipolar configurations, sometimes proposed as a mechanism for eruptive solar events, probably requires either fully three-dimensional field configurations or nonzero plasma pressure. The results apply only to fields that are strictly bipolar, and do not rule out equilibrium loss in more complex structures such as quadrupolar fields.